Margret Giesen

Step and island dynamics at solid/vacuum and solid/liquid interfaces

Abstract The investigation of step and island dynamics on surfaces has enormously contributed to the microscopic understanding of mass transport processes in equilibrium, during growth and coarsening of surface structures. From the scaling behavior of step fluctuations as well as of the ripening of mono- and multilayer islands, the atomic diffusion processes may be unambiguously determined even when single atom motion cannot be observed directly. This is the case for metal surfaces at high temperatures and, in particular, for metal electrodes in electrochemical environment. In the case of the latter, the analysis of step and island dynamics is the only method available to date to learn about the dynamics at the solid/liquid interface on the atomic scale. Here, we review the basic theoretical principles and the experimental contributions on step and island dynamics performed in ultra-high vacuum as well as (more recently) in electrolyte. It focuses also on the comparison between experimental results obtained at the solid/vacuum and at the solid/liquid interface.

Step dynamics on Ag(111) and Cu(100) surfaces

Abstract Tunnel images of steps on Ag(111) and Cu(100) display a particular kind of micro-roughness (“frizzes”). We have investigated the frizzes as a function of time and substrate temperature. By comparison to a model for kink diffusion we show that the frizzes are caused by kink motion which is rapid on the time scale of a tunnel image. On vicinal surfaces such as Cu(1111) kinks move less rapidly.

What does one learn from equilibrium shapes of two-dimensional islands on surfaces?

The equilibrium shape of islands has been determined with high accuracy as a function of temperature for Cu(100), Cu(111) and Ag(111)-surfaces. The equilibrium shape is analyzed using the inverse Wulff-construction, the Ising-model, and two novel methods concerning the minimum curvature and the aspect ratio of islands. From the conventional inverse Wulff-construction, the angle dependence of the step free energy is obtained. On Cu(111) and Ag(111), the energies of A- and B-type steps differ only by about 1%. The analysis of the data using the analytical form of the equilibrium shape provided by the Ising-model yields quite acceptable values for the kink energy on (111)-surface s, but not on the (100)-surface. It is shown that the reason for the failure is due to the different ratio of kink and step energies assumed in the Ising-model for the two surfaces. By combining well-known relations on the statistical mechanics of steps and islands, a simple relation between the kink energy and the minimum curvature of the equilibrium shape is derived and the experimental data are analyzed accordingly for the kink energies on all surfaces. On the Cu(100)-surface, the kink energy compares well with an earlier independent experimental result. The temperature dependence of the free energy of the 100% kinked step in (100)- and (111)-islands is calculated theoretically using general principles. The theory is used to determine the absolute values of the step energies from the experimental data.

Potential-induced stress in the solid-liquid interface: Au(111) and Au(100) in an HClO4 electrolyte

Abstract The cantilever bending method is applied to the determination of the potential-induced interface stress for Au(111) and Au(100) in 0.1M HClO4. The bending of the crystal plates was observed using an electrochemical STM. By a reconsideration of the elasticity theory of bending, it is shown that the entire interface including the liquid part contributes to the measured stress. The potential-induced lifting of the reconstruction of the two surfaces was observed using the STM simultaneously with the measurement of the interface stress. By making use of the fact that after cycling the potential between −140 and 960 mV versus SCE the surfaces remain in an unreconstructed state, one can determine independently the stresses which are associated with the surface reconstruction and with the specific adsorption of ClO−4 ions. The stress induced by the specific adsorption is comparable in size to the adsorption-induced stress for surfaces in vacuum. The reconstruction-related changes in the surface stress are discussed in the context of theoretical models for the reconstruction. The results support the notion that the stress is the driving force for the reconstruction on Au(111), whereas on Au(100) stress relaxation associated with the reconstruction is not a sufficient source of energy to force the surface into the reconstructed state.

Decay of Cu adatom islands on Cu(111)

We have investigated the decay of Cu adatom islands on Cu(111) as a function of temperature using scanning tunneling microscopy. By comparing the experimental results with the theory of Ostwald ripening and with numerical simulations we find that the decay is limited by the diffusion of adatoms on the terrace. From the decay rate at constant island size as a function of temperature, the sum of the energy for the formation of an adatom on the terrace and the activation energy for diffusion on the terrace is found to be 0.78±0.04 eV. The local environment has a significant influence on the shape of the island area versus time curves. An optimum match between simulations and experiment for the shape of the decay curves is achieved for a line tension of the islands of 0.45 eV per atom length. The Schwoebel-Ehrlich barrier for the hopping of atoms over a step is determined to be about 0.12 eV by matching the relative decay times of islands on small terraces to the simulations.

Step fluctuations on metals in contact with an electrolyte: a new access to dynamical processes at the solid/liquid interface

Abstract We have measured the equilibrium step fluctuations on a stepped Ag(111) surface in an aqueous electrolyte as a function of the electrode potential. In the regime of negative potentials with respect to the saturated calomel electrode the time dependence of the step fluctuations obeys a t 1 4 - power law with no dependence of the fluctuations on the step-step distance. This is evidence for a mass transport restricted to the step edges. In the regime of positive potentials, the time dependence obeys a t 1 2 - power law and the fluctuations depend on the step-step distance. This is evidence for a rapid exchange of step atoms with the terraces and an exchange of the adatoms on the terraces with the electrolyte. The step fluctuations increase exponentially with the potential before silver begins to dissolve.

Step fluctuations on Pt(111) surfaces

Abstract We have investigated the temperature dependence of equilibrium fluctuations of monatomic steps on Pt(111) surfaces using space and time correlation functions. From the spatial correlation function of steps we have determined a kink energy of 0.167 ± 0.005 eV for steps with (100) orientation. The same value was found for steps with (111) orientation. The time dependence of the correlation function obeys a t 1 4 power law, provided that the mean square of the fluctuations is in the macroscopic limit. The t 1 4 power law is indicative of mass transport along the steps. From the temperature dependence of the time fluctuations an activation energy of 1.0 ± 0.16 eV is determined for the hopping of atoms along steps of either orientation.

Step-step interaction energy on vicinal copper surfaces

Abstract Measurements are presented of the terrace width distribution on a vicinal copper surface with (1 1 13) orientation as a function of temperature. Assuming a mean field model, we determine the strength of the step-step interaction from the width of a Gaussian fit. Based on the value for the strength of interaction, the expected terrace width distributions for Cu (1 1 7) and Cu (1 1 11) at room temperature are calculated and compared to earlier measurements on these surfaces. in addition, an analysis of a data set of STM images of the Cu (1 1 19) surface at temperatures above room temperature is discussed. All of the experimental data are well described by the measured value for the step-step interaction strength on the Cu (1 1 13) surface. From the interaction strength we obtain a rough estimate of the roughening temperatures of Cu (11 n ) surfaces.

Influence of anion adsorption on the step dynamics on Au (111) electrodes

Abstract Using scanning tunneling microscopy, we have investigated the step dynamics on an Au(111) single crystal electrode in aqueous electrolytes. Our studies focused on the influence of specifically adsorbed anions and the anion concentration on the mobility of gold atoms at monatomic-high step edges. The experiments were performed in chloride-containing and chloride-free H 2 SO 4 electrolytes. From the quantitative analysis of equilibrium step fluctuations we deduce the dominant mass transport mechanisms as a function of the electrode potential and as a function of the anion concentration. Estimates of the energies involved in the mass transport are presented.

Orientation dependence of the Cu(001) surface step stiffness: Failure of solid-on-solid and Ising models to describe experimental data

We have investigated the step stiffness on Cu(001) surfaces as a function of step orientation by two independent methods at several temperatures near 300 K. Both sets of data agree well and show a substantial dependence of the stiffness on the angle of orientation. With the exception of steps oriented along , the experimental stiffness is significantly larger than the stiffness calculated within the solid-on-solid model and the Ising model, even if next-nearest-neighbor interactions are taken into account. Our results have considerable consequences for the understanding and for the theoretical modeling of equilibrium and growth phenomena, such as step meandering instabilities.